This question is somehow related to my previous one or even could be considered as a continuation of that. As I described in my previous question, I'm hired for my current position in a university in the US by somebody that left our university for another position more than a year ago. Someone else in our organization was assigned as an interim supervisor to be my manager, which some of her actions and her hostility towards my previous supervisor described in the previous question. One quick note here is that my current supervisor doesn't have any experience or educational background in the tasks defined for my position. In fact, my position was supposed to be abolished when my previous supervisor left our organization, but somehow our CIO decided to just put a random person to take the role of the previous supervisor in order to buy more time to think about if they want to really abolish my position altogether or not.
Recently, I received a long email from my current supervisor that says she is frustrated and overwhelmed by her main duties in our organization which is not related to my position or tasks defined for me and doesn't have any time to review my work. She thinks my work quality is low and she could do it much better herself and she needs to spend lots of time reviewing/correcting my submitted works to her, which of course I would say that's not correct. She sends my materials back to me without even adding a single line to them or changing anything and then claims that she spent a whole day correcting them. At least, I think I know what I'm doing after being in my current position for more than 3 years and I didn't receive even a single complaint about my work or its quality from my previous supervisor, who has a Ph.D. directly related to tasks defined for my role.
One another complaint of my current supervisor is that I submit materials to her for review too late close to the deadlines and she wants me to submit materials to her at least 5 days before the deadlines. It just surprises me because I always submit my work to her at least a week before deadlines but she doesn't respond to me or doesn't send me her feedback until the night before the deadline and she accuses me that my submission is late and she has lots of things to do other than reviewing my work.
Finally, I submitted my work to her this Monday that there is a deadline until next Monday and still I did not receive any response from my supervisor. I'm pretty sure that I would receive a long email, full of complaints, just the night before the deadline.
I feel I'm abandoned and somehow abused by my current supervisor and I think I'm not really welcome in this organization. I think the best action for me was to leave after my previous supervisor left and staying in my current position after him with the current situation was the worst decision.
So my question is: how do I deal with my current supervisor? I'm thinking to bypass my current supervisor and have a meeting with our executive director to discuss these things. But, I'm not sure if that would help or not cause I have never talked to him before. Any idea or suggestion is appreciated and please excuse me for such a long question.